Factor x^2 + y^2 = 25, x = y -1

I have to factor this and work out the point of intersections and please show the working out so i could understand.

x² + y² = 25
( x + y ) ( x - y ) = 5²
Hey you did say you had to factorize it .......

x² + y² = 25
x = y - 1

(y-1)² + y² = 25
y² - 2y + 1 + y² = 25
2y² - 2y -24 = 0
2 ( y - 4 ) ( y + 3 ) = 0
y=4 and x=3
y=-3 and x=-4
( 3 , 4 ) and ( -4 , -3 ) are your points of intersection.